Details

sample98.0ms

Algorithm

intervals

Results

27.0ms	256×	body	80	valid
27.0ms	291×	body	80	nan

simplify36.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	50	17
1	106	17
2	374	17
3	1652	17
4	5001	17

prune6.0ms

Filtered

1 candidates to 0 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 5.0b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* z (sqrt (+ t a)))
0.3b	(/ 2.0 (* t 3.0))
2.7b	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
6.1b	(/ (* z (sqrt (+ t a))) t)

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

20×	`frac-sub`
16×	`add-exp-log` `add-cbrt-cube`
15×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`flip3--` `flip--`
8×	`frac-times` `associate-*r/`
7×	`associate-r`
6×	`pow1` `times-frac` `associate--r+` `add-log-exp`
5×	`flip3-+` `sqrt-prod` `flip-+`
4×	`cbrt-undiv` `sqrt-div` `div-exp` `associate-/r` `associate-/l`
3×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-l` `prod-exp` `cbrt-unprod`
2×	`frac-2neg` `associate-*l/` `associate--l+` `clear-num` `div-inv` `associate-/l/` `unswap-sqr`
1×	`diff-log` `pow-prod-down` `*-commutative` `distribute-lft-out`

Counts

4 → 101

Calls

4 calls:

7.0ms	(* z (sqrt (+ t a)))
5.0ms	(/ 2.0 (* t 3.0))
13.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
7.0ms	(/ (* z (sqrt (+ t a))) t)

series82.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(* z (sqrt (+ t a)))
2.0ms	(/ 2.0 (* t 3.0))
49.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
19.0ms	(/ (* z (sqrt (+ t a))) t)

simplify43.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1012	1260
1	5001	1212

prune236.0ms

Filtered

113 candidates to 88 candidates (22.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	109	4	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	110	4	114

Merged error: 0.5b

Counts

114 → 4

localize31.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt t)
0.5b	(cbrt t)
1.6b	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))
2.7b	(- (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
60×	`frac-sub`
58×	`times-frac`
47×	`*-un-lft-identity`
46×	`associate-r`
39×	`frac-times`
35×	`add-cube-cbrt`
31×	`cbrt-prod`
28×	`sqrt-prod`
27×	`associate-*r/`
25×	`add-exp-log` `flip3--` `flip--`
21×	`associate-*l/`
18×	`add-cbrt-cube`
10×	`unswap-sqr`
9×	`flip3-+` `flip-+`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp` `associate-l`
6×	`pow1` `distribute-lft-out` `associate--r+` `add-log-exp`
3×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
2×	`pow1/3` `associate--l+` `div-inv`
1×	`diff-log` `pow-prod-down` `*-commutative`

Counts

4 → 169

Calls

4 calls:

1.0ms	(cbrt t)
1.0ms	(cbrt t)
22.0ms	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))
19.0ms	(- (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))

series120.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt t)
22.0ms	(cbrt t)
20.0ms	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))
57.0ms	(- (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))

simplify65.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1754	3649
1	5002	3540

prune406.0ms

Filtered

181 candidates to 144 candidates (20.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	181	0	181
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	181	4	185

Merged error: 0.5b

Counts

185 → 4

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 2.0 (* t 3.0))
3.3b	(log (exp (/ 2.0 (* t 3.0))))
3.8b	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (log (exp (/ 2.0 (* t 3.0)))))))
6.1b	(/ (* z (sqrt (+ t a))) t)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log` `add-cbrt-cube`
11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
8×	`log-pow` `frac-sub`
7×	`exp-prod` `flip3--` `flip--`
6×	`associate--r+` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `frac-times` `associate-r/` `div-exp` `associate-/r` `associate-/l*`
3×	`distribute-rgt-in` `sub-neg` `log-prod` `distribute-lft-in` `div-inv`
2×	`frac-2neg` `sqrt-div` `associate-*l/` `prod-exp` `associate--l+` `clear-num` `cbrt-unprod` `associate-/l/`
1×	`flip3-+` `diff-log` `rem-log-exp` `flip-+`

Counts

4 → 89

Calls

4 calls:

5.0ms	(/ 2.0 (* t 3.0))
4.0ms	(log (exp (/ 2.0 (* t 3.0))))
13.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (log (exp (/ 2.0 (* t 3.0)))))))
8.0ms	(/ (* z (sqrt (+ t a))) t)

series75.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(/ 2.0 (* t 3.0))
2.0ms	(log (exp (/ 2.0 (* t 3.0))))
54.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (log (exp (/ 2.0 (* t 3.0)))))))
16.0ms	(/ (* z (sqrt (+ t a))) t)

simplify82.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	763	1016
1	3784	927
2	5001	926

prune210.0ms

Filtered

101 candidates to 79 candidates (21.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	101	4	105

Merged error: 0.5b

Counts

105 → 4

localize33.0ms

Local error

Found 4 expressions with local error:

2.3b	(* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))
2.8b	(* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0))
7.0b	(- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0)))))
26.9b	(/ (- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))) (* t (* (- a (/ 5.0 6.0)) (* t 3.0))))

rewrite202.0ms

Algorithm

rewrite-expression-head

Rules

766×	`associate-*l/`
764×	`associate-*r/`
524×	`frac-sub`
498×	`flip3--` `flip--`
364×	`frac-times`
240×	`sqrt-div`
162×	`associate-/l/`
120×	`flip3-+` `flip-+`
28×	`add-exp-log` `add-cbrt-cube`
16×	`distribute-rgt-in` `distribute-lft-in`
14×	`pow1`
12×	`prod-exp` `cbrt-unprod`
9×	`sub-neg`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `associate--r+`
7×	`associate-l`
6×	`pow-prod-down` `add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`times-frac` `associate-/l*`
2×	`associate-r` `associate-/r/` `*-commutative`
1×	`frac-2neg` `diff-log` `div-sub` `clear-num` `associate-/r*` `div-inv` `difference-of-squares`

Counts

4 → 437

Calls

4 calls:

22.0ms	(* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))
7.0ms	(* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0))
33.0ms	(- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0)))))
57.0ms	(/ (- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))) (* t (* (- a (/ 5.0 6.0)) (* t 3.0))))

series470.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))
7.0ms	(* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0))
167.0ms	(- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0)))))
249.0ms	(/ (- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))) (* t (* (- a (/ 5.0 6.0)) (* t 3.0))))

simplify306.0ms

Algorithm

egg-herbie

Counts

449 → 449

Iterations

Useful iterations: 1 (94.0ms)

Iter	Nodes	Cost
0	4640	24427
1	5001	24209

prune10.8s

Filtered

449 candidates to 410 candidates (8.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	448	1	449
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	448	5	453

Merged error: 0.2b

Counts

453 → 5

regimes744.0ms

Accuracy

-6.2% (2.3b remaining)

Error of 2.8b against oracle of 0.5b and baseline of 2.6b

bsearch120.0ms

Steps

Iters	Range		Point
8	9.993274792250503e-119	1.2500776669285984e-115	4.2989924261091155e-116
7	-1.636586815708768e-105	-9.268939291488634e-107	-4.648042522474214e-106

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	56
1	79	56

end0.0ms

sample2.7s

Algorithm

intervals

Results

767.0ms	8000×	body	80	valid
752.0ms	8157×	body	80	nan

Details

sample98.0ms

simplify36.0ms

prune6.0ms

localize23.0ms

rewrite36.0ms

series82.0ms

simplify43.0ms

prune236.0ms

localize31.0ms

rewrite53.0ms

series120.0ms

simplify65.0ms

prune406.0ms

localize28.0ms

rewrite32.0ms

series75.0ms

simplify82.0ms

prune210.0ms

localize33.0ms

rewrite202.0ms

series470.0ms

simplify306.0ms

prune10.8s

regimes744.0ms

bsearch120.0ms

simplify2.0ms

end0.0ms

sample2.7s

Profiling